A Note on the Mathematical Theory of the Multielectrode Tube

The expression for the a-c current (rather the change in current due to applied a-c voltages) in any electrode is expanded in an ascending power series in terms of all the applied a-c voltages. It is shown that the coefficients in these series must satisfy a number of systems of linear simultaneous equations (one system for each power and frequency of the terms), and that hence to obtain the coefficients in any particular case it is merely necessary to set up these equations and solve them. The solution of the equations of course increase in complexity as the number of electrodes increases. The development does not make any assumptions of approximations, although in the discussion only the terms of the first and second degree are considered. It is shown, however, that however slow be the convergency of the series, the coefficients must always satisfy similar sets of algebraic equations.